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Worksheet/Answer keyLinear equations

Worksheet/Answer keyLinear equations

WV.M.8.EE. Expressions and Equations

Understand the connections between proportional relationships, lines, and linear equations.

M.8.7. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. (e.g., Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.)

M.8.8. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

WV.M.8.F. Functions

Define, evaluate, and compare functions.

M.8.13. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. (e.g., The function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.)

Use functions to model relationships between quantities.

M.8.14. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

WV.M.1HS8. 8th Grade High School Mathematics I

Relationships between Quantities

Create equations that describe numbers or relationships.

M.1HS8.6. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Linear and Exponential Relationships

Define, evaluate, and compare functions.

M.1HS8.14. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. (e.g., The function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.)

Understand the concept of a function and use function notation.

M.1HS8.18. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Interpret functions that arise in applications in terms of a context.

M.1HS8.20. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

M.1HS8.22. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Analyze functions using different representations.

M.1HS8.23. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

M.1HS8.23.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

Construct and compare linear, quadratic, and exponential models and solve problems.

M.1HS8.28. Distinguish between situations that can be modeled with linear functions and with exponential functions.

M.1HS8.28.a. Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.

WV.M.A18. High School Algebra I for 8th Grade

Relationships between Quantities and Reasoning with Equations

Create equations that describe numbers or relationships.

M.A18.6. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Linear and Exponential Relationships

Define, evaluate and compare functions.

M.A18.21. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. (e.g., The function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.)

Use functions to model relationships between quantities.

M.A18.25. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Interpret functions that arise in applications in terms of a context.

M.A18.27. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

M.A18.29. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Analyze functions using different representations.

M.A18.30. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

M.A18.30.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

Construct and compare linear, quadratic, and exponential models and solve problems.

M.A18.35. Distinguish between situations that can be modeled with linear functions and with exponential functions.

M.A18.35.a. Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.

Expressions and Equations

Create equations that describe numbers or relationships.

M.A18.56. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Quadratic Functions and Modeling

Interpret functions that arise in applications in terms of a context.

M.A18.64. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

M.A18.66. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Analyze functions using different representations.

M.A18.67. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

M.A18.67.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.

Standards